Lila flies a drone in the direction of 90° towards Avery. Once she gets to Avery she changes course and flies in the direction of 200° towards Mark. Lila and Avery are 20 feet apart; Mark and Avery are 30 feet apart. How far apart are Mark and Lila?

29.8ft

Step-by-step explanation:

suppose that the angles are measured from an x-axis.

we know that:

Lila and Avery are 20 feet apart.

Mark and Avery are 30 feet apart.

If we locate the position of Lila in the (0, 0)

and we use the relation:

x = r*cos(θ) and y = r*cos(θ)

Then the position of Avery is:

P = (20ft*cos(90°), 20ft*sin(90°)) = (0, 20ft)

and the position of mark will be:

P = (0 + 30ft*cos(200°), 20ft + 30ft*sin(300)) = (-28.2ft, 9.7ft)

And because Lila is at the origin, the distance between Mark and Lila is equal to the module of that vector,

Distance = √((28.2ft)^2 + (9.7ft)^2) = 29.8ft

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497